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## Re: Diatonic notation system

 From: Hans Aberg Subject: Re: Diatonic notation system Date: Mon, 8 Dec 2008 22:01:22 +0100

```On 8 Dec 2008, at 12:28, Graham Breed wrote:

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```Are you on board with the regular mapping paradigm?  I may as well
promote it while I'm here.

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I looked a bit at it, the section "The Core Paradigm". The model I indicated also chooses some generators, but in addition reflects the notion of scale degrees that the Western musical notation system brings out, which in its turn relies on an underlying empiric principle, also in the case when augmented with intermediate pitches as in Persian and Arab music:
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Given intervals x (resp. y) in a two (resp. three) generator model x = p m + q M (resp. y = p m + q M + r n), define a scale degree deg x = p + q (resp. deg y = p + q + r). Empirically, melodic development normally takes place between different scale degrees, also on say chromatically altered ornaments. This is also true in the Persian dastgahs, using Farhat's description. If one alters scale degrees, melodic development still normally takes place between different scale degrees, as on a parallel, altered scale. In the Western notation system, one achieves this by simply minimizing the amount of temporary accidentals, if the notes are not too chromatically dense, which is very intuitive.
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Now, the construction on the link above seems to ignore those scale degrees. If one defines a scale from say an octave P8 and a perfect fifth P5, then scale degrees can be defined by setting deg P8 = 7, deg P5 = 4, and then work it out for other combinations. This gives deg M = deg (2 P5 - P8) = 2 deg P5 - deg P8 = 1, deg m = deg (P4 - 2 M) = deg (P8 - P5 - 2M) = 7 - 4 - 2 = 1.
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Then, in addition, to get an (extended) Western notation system, one must define pitches A B C D E F G ... of scale degrees 0, 1, .., (n-1), where n is the number of scale degrees in what is called an "octave".
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Hans

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